Community Formation in Wealth-Mediated Thermodynamic Strategy Evolution

TL;DR

This paper models strategy evolution in a spatial game using a thermodynamic approach, revealing how community structures form and change with temperature and payoff dynamics.

Contribution

It introduces a novel thermodynamic framework for analyzing strategy updates in spatial games, deriving conditions for community formation and boundary behavior.

Findings

Community formation depends on payoff and temperature parameters.

Higher temperature leads to more boundary drifting and less stable communities.

Numerical simulations reveal unexpected behaviors in strategy dynamics.

Abstract

We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale which defines the random fluctuations. Players with higher bank values are thus less likely to change strategy than players with lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of temperature increase on the underlying system, and identify surprising properties of this model through numerical simulations.